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      Transverse Mercator Projection
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	  content="transverse Mercator projection,
		   Gauss-Krueger projection,
		   universal transverse Mercator,
		   UTM,
		   conformal projections,
		   WGS84 ellipsoid,
		   latitude and longitude" />
    <meta name="author" content="Charles F. F. Karney" />
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    <h3>Transverse Mercator Projection</h3>
    <p>
      This page is a web resource for the paper
      <blockquote>
	Charles F. F. Karney,<br>
	<a href="https://doi.org/10.1007/s00190-011-0445-3">
	<i>Transverse Mercator with an accuracy of a few nanometers</i></a>,<br>
	J. Geodesy <b>85</b>(8), 475&ndash;485 (Aug. 2011);<br>
	preprint <a href="https://arxiv.org/abs/1002.1417">arXiv:1002.1417</a>
	(<a href="https://arxiv.org/pdf/1002.1417">pdf</a>);<br>
	<a href="tm-addenda.html">addenda</a>.
      </blockquote>
      The implementation of the series and exact algorithms are
      available as part of GeographicLib which is licensed under the
      <a href="http://www.opensource.org/licenses/MIT">MIT/X11 License</a>;
      see <a href="html/LICENSE.txt">LICENSE.txt</a> for the terms.
    </p>
    <ul>
      <li>
	<a href="index.html">GeographicLib home page</a>
      <li>
	<a href="html">GeographicLib documentation</a>
	<ul>
	  <li>
	    The C++ class
	    <a href="html/classGeographicLib_1_1TransverseMercator.html">
	      TransverseMercator</a>, which implements the Kr&uuml;ger
	    series method.
	  <li>
	    The C++ class
	    <a href="html/classGeographicLib_1_1TransverseMercatorExact.html">
	      TransverseMercatorExact</a>, which implements the Lee's exact
	    method.
	  <li>
	    The utility
	    <a href="html/TransverseMercatorProj.1.html">
	      TransverseMercatorProj</a>, for testing the implementations.
	  <li>
	    The utility
	    <a href="html/GeoConvert.1.html">
	      GeoConvert</a>, for UTM and MGRS conversions and an
	    <a href="cgi-bin/GeoConvert">
	      online coordinate converter</a>.
	</ul>
      <li>
	<a href="https://sourceforge.net/projects/geographiclib/files/distrib">
	  Download GeographicLib</a>
    </ul>
    <p>
      Additional material:
    </p>
    <ul>
      <li>
	A good way to visualize the transverse Mercator projection
	over the entire global is using
	<a href="tm-grid.kmz"
	   type="application/vnd.google-earth.kmz"> tm-grid.kmz</a>,
	which is a Google Earth KML file showing the transverse
	Mercator grid (in red) for the WGS84 ellipsoid with grid
	spacing 1000 km in the <i>x</i> and <i>y</i> directions.  The
	scale, <i>k</i> = 0.9998035, has been adjusted so that the
	distance from the equator to a pole is 10000 km.<br>  If you
	open the "tm-grid" folder in Google Earth and check on the
	"spherical-transverse-mercator" subfolder, you will also see
	the corresponding spherical transverse Mercator grid (in
	yellow) conformally mapped to the WGS84 ellipsoid.  (This
	doesn't have a constant scale on the central meridian.)
      <li>
	<a href="https://doi.org/10.5281/zenodo.32470">
	  <i>Test data for the transverse Mercator projection</i></a> <br>
	Use only the entries with latitude &ge; 0 for testing an
	algorithm with the standard convention for the branch cut.
      <li>
	Maxima implementation of Lee's exact method (arbitrary precision):
	<a href="html/tm.mac">tm.mac</a>
	and <a href="html/ellint.mac">ellint.mac</a>.  There is brief
	documentation at the top of tm.mac.
      <li>
	The paper gives  Kr&uuml;ger's series accurate to 8th order;
	<ul>
	  <li>
	    <a href="html/transversemercator.html#tmseries">
	      Kr&uuml;ger's series to 10th order</a>;
	  <li>
	    Kr&uuml;ger's series to 30th order,
	    <a href="html/tmseries30.html">tmseries30.html</a>;
	  <li>
	    Maxima code to generate Kr&uuml;ger's series to arbitrary order,
	    <a href="html/tmseries.mac">tmseries.mac</a> (there is brief
	    documentation at the top of the file);
	  <li>
	    <a href="http://maxima.sourceforge.net/">download maxima</a>.
	</ul>
      <li>
	<a href="https://doi.org/10.2312/GFZ.b103-krueger28">
	  Kr&uuml;ger's 1912 paper</a>.
      <li>
	<a href="https://doi.org/10.3138/X687-1574-4325-WM62">
	  Relevant section of Lee's 1976 paper</a> (price $15).
    </ul>
    <hr>
    <address>Charles Karney
      <a href="mailto:charles@karney.com">&lt;charles@karney.com&gt;</a>
      (2017-09-30)</address>
    <br>
    <a href="https://geographiclib.sourceforge.io">
      GeographicLib home
    </a>
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